The Kinetic Molecular Theory

Course Outline General Chemistry--Unit 2 04/25/09

The Kinetic Molecular Theory Description of Mixtures �Before You Begin: To master this material you will need to understand kinetic molecular theory and know the types of intermolecular attractions.

Types of Mixtures A mixture is a sample of matter in which two or more different substances are physically combined such that each retains its own identity. The properties of a mixture are an average of the properties of the components of that mixture. For example, if you add sugar and water together you get a sugar water mixture. The mixture will be a colorless liquid with density, viscosity, boiling point and vapor pressure almost the same as that of pure water. It will taste sweet like sugar. When the water evaporates, sugar crystals will form. Neither the sugar nor the water will have been fundamentally changed during the process. In contrast, when two or more substances are chemically combined, a new substance is formed. This new substance has properties that may be quite different from the properties of the substances that were used to produce it. If yeast is added to the sugar water mixture, the single celled organisms will digest the sugar and use it to produce carbon dioxide, ethanol, and energy. The substances that result are very different from those of the sugar that the yeast ingested. A homogeneous mixture, also called a solution, is a mixture in which the substances are uniformly blended on the smallest scale. A homogeneous mixture ‘looks like’ one substance, because it is so uniform. Air is an example of a homogeneous mixture. Air is a mixture of gases, mostly nitrogen and oxygen with small amount of carbon dioxide, water vapor and other gases. The solvent is the major component of a solution (the part that does the dissolving). The solute is the minor component(s) of the solution (the part that gets dissolved). A heterogeneous mixture is one in which the substances are not uniformly mixed.

These mixtures often look “lumpy” because we can see the different constituents. Concrete is an example of a heterogeneous mixture made up of rock, sand, and cement. A colloidial suspension or colloid is a mixture in which the substances are uniformly mixed on a large scale, but these mixtures have particles which are too large and will eventually separate. Fog and milk are examples of colloids. Like other colloids, fog and milk have a cloudy appearance, because colloids exhibit the Tyndall Effect. The individual particles that make up a colloid are too small too see, but they are large enough to scatter the light that passes through them. We can see a car’s headlights from the side in the fog because a beam of light is scattered due to the Tyndall Effect.

Examples of Mixtures of the Various States of Matter Before you begin this material, you need to understand the kinetic molecular theory description of the states of matter and gas law calculations from unit 2.

Gas as a Solute Although people tend to think of solutions as solids dissolved in liquids, mixtures of gases are solutions. They are homogeneous because gases diffuse throughout their container keeping the mixture ‘mixed.’ Air is a mixture of gases that varies in composition with weather and altitude, but, in any given area, it is a uniform mixture composed of nitrogen and oxygen with traces of other gases. The Composition of Air Gas Percent by Volume in Dry Air Nitrogen 78.084 Oxygen 20.964 Argon 0.934 Carbon 0.035 Dioxide Neon 0.0018 Helium 0.00052

Methane, CH4 Krypton Hydrogen

0.00017 0.00011 0.00005

This data is from Earth Fact Sheet, by NASA. The amount of water in the atmosphere varies (hot air can hold more water vapour than cold air) but totals roughly 1 percent.

Gaseous Mixtures and Dalton’s Law of Partial Pressure Dalton’s law of partial pressures states that for a mixture of ideal gases the total pressure of the mixture will be equal to the sum of each gas’s partial pressure, the pressure it would exert under the same conditions of volume and temperature if that gas were alone in the container.

This law implies that any gas in a mixture of gases behaves independently of the others. Kinetic molecular theory explains that gas particles are not attracted to or repelled by one another. When they collide with each other or the walls of their container, they bounce elastically. Because the total number of collisions depends on the number of collisions of all of the different types of particles, the total pressure equals the sum of each gas’s individual pressure. If the gases are not ideal, when they collide they interact (perhaps by reacting chemically or by sticking together due to intermolecular force). In that case, the pressure would be lower than that predicted by Dalton’s law. Concept Check: Three gases are in a container, A, B, and C. Each has the same partial pressure. The container is cooled below the boiling point of the gas B, which then condenses into a liquid. What effect does this have on the total pressure and the partial pressures of each gas? Answer: The partial pressure of gas B drops radically. A liquid phase does not contribute to the pressure of a gas except for its vapor pressure (the pressure due to the small amount of liquid that evaporates in a closed container). The partial pressures of A and C do not change because the behavior of an ideal gas is independent of the presence (or absence) of other ideal gases. The total pressure drops by an amount equal to the difference between the original pressure of gas B and its vapor pressure.

Aerosols The components of a mixture do not have to be the same phase. Fog is an example of a liquid (water) suspended in a gas (air). Smoke is an example of a mixture in which the solutes are solids, liquids, and gases while the solvent is a gas (air). When organic material burns it combines with oxygen to form nonmetal oxides, especially carbon dioxide and water vapor. These are gases. Inadequate supplies of oxygen lead to the breakdown of the organic material into a complex mixture of other compounds. According to the 1964 Surgeon General’s

Report on Smoking and Health “The particulate matter of MS [mainstream cigarette] smoke contains at least 3,500 individual compounds.” The fine particles and droplets form a suspension which scatters light by the Tyndall effect giving smoke a hazy appearance. Mixtures composed of particles of solids/liquids suspended in a gas are called aerosols. Climate change theorists estimate that about 10% of the atmosphere’s aerosols are due to human activities (such as burning fossil fuels) as opposed to natural events (such as volcanic eruptions). Some computer models project that the atmosphere may cool due to reduction is transmitted solar radiation by atmospheric aerosols.

Liquid as a Solute Gases in a Liquid and Henry’s Law Gases can mix with liquids to form heterogeneous mixtures like whipped cream. They can also dissolve in a liquid to form a solution. The solubility of a gas in a liquid depends on the nature of the substances involved and on the pressure of the gas. Henry’s law states that the concentration of the dissolved gas is directly proportional to its pressure:

where C is the concentration of the gas, P is the pressure of the gas, and k is a proportionality constant that is unique for each gas/liquid combination and varies with temperature. Kinetic molecular theory can help explain Henry’s law. If a gas is in contact with the surface of a liquid, the gas particles collide with the liquid particles. Some of these collisions are elastic, but, in some cases, the gas particles with lower than average kinetic energy will not be able to overcome the intermolecular attraction of the liquid. Some gas particles will stick to and mix with the liquid. The number of collisions increases as the pressure increases, so an increase in pressure increases the concentration of dissolved gas. The constant, k, is different for each combination of liquid and gas because the strength of the intermolecular force depends on factors such as polarity and the size of the molecule. The value of k also varies with temperature. As temperature increases, the kinetic energy of the gas particles increases, and fewer of the collisions result in solution.

Concept Check: Carbonated beverages are bottled so that greater than one atmosphere of carbon dioxide is in the container. Describe what happens on a molecular level when a can of soda pop is opened. Answer: The unopened can has a relatively high pressure of carbon dioxide gas compared to the amount of carbon dioxide partial pressure in the air. Gaseous carbon dioxide molecules strike the liquid, and the ones with low kinetic energy cannot escape the intermolecular attractions. These become part of the liquid phase. At the same time, some of the dissolved carbon dioxide molecules have enough kinetic energy to escape the attractions of their neighbors and vaporize. These processes are in equilibrium (happening at the same time and at the same

rate). When the can is opened, the pressure of the carbon dioxide drops because the partial pressure of carbon dioxide in air is low. At lower pressure there are fewer collisions between the gaseous carbon dioxide and the liquid. Fewer collisions mean that fewer of the carbon dioxide molecules dissolve. However, the vaporization of dissolved carbon dioxide is still occurring. This net imbalance upsets the equilibrium and causes the carbon dioxide to leave the solution in bubbles as though it were boiling.

Concept Check: Estimate the percent of dissolved carbon dioxide left in an opened can of soda pop compared to an unopened can if it was bottled under 1.0 atm of pure carbon dioxide. Assume the room temperature is the same as the temperature during bottling. Answer: To estimate the percentage of carbon dioxide left, we have to make a few assumptions. We need to know the partial pressure of carbon dioxide in air. The total pressure of the air at sea level is about 1 atm, and the atmosphere is 0.035 % carbon dioxide by volume (see table above). If we assume that the composition of the atmosphere is uniform (it isn’t), 100 L of air would have 0.035 L of carbon dioxide in it (let’s ignore the significant figures issues, since this is just an estimate). Assuming that carbon dioxide is an ideal gas, then 1 mol has a volume of 22.4 L at STP. Therefore, 0.035 L of carbon dioxide is 1.6x10-3 moles. In a total volume of 100 L, the partial pressure due to the carbon dioxide is

A can of soda doesn’t hold 100L, but the partial pressure is the relative amount of carbon dioxide in 1 atm of air and is independent of the volume. By Henry’s law,

where C is the concentration, P is the pressure and k is a constant. But Henry’s law is true under the first set of conditions (unopened) and the second set of conditions (opened), and k is the same as long as the temperatures were the same. The percent of the carbon dioxide left after opening is (C2/C1)100.

This means that 99.96% of the carbon dioxide bubbles away! Well, really it means that all of it (100%) bubbles away because our estimate has only one significant

figure.

Solutions and Solubility A liquid or solid dissolved in water to form a homogeneous mixture is what most of us think of first when we think of the term solution (well, we think of this second, right after thinking of a solution as an answer to a problem!). This type of mixture is an aqueous solution and is very important to life as we know it and to learning chemistry. We will describe these mixture is a lot more detail. For now, we will think in general terms of the behavior of the general class of homogeneous mixtures with a liquid solvent. The particles that make up a gas move throughout their container. For a mixture of gases, this molecular motion keeps the mixture uniform. The molecules of a liquid do not move very far with respect to one another. The result is that a liquid phase mixture needs a mechanism to stay mixed. Suppose we use kinetic molecular theory to explain the behavior of a mixture of liquids, oil and water for example. The molecules of water are attracted to each other by induced dipole forces and strong hydrogen bonds. At room temperature and pressure these attractions are stronger than the molecular kinetic energy, so the water is a liquid. Oil is non-polar, so its only intermolecular force is induced dipole attraction. The oil molecules have high formula weight. Their molecular geometry is long chains of single and double bonded carbon atoms with enough hydrogen atoms to fill their octet requirements. These long chains hold an induced dipole for a relatively long time. They also tend to tangle up with one another, making oil more viscous than water. Oil molecules tend to tangle up with other oil molecules and water tends to hydrogen bond with other water molecules. When we blend oil and water together the intermolecular attractions for oil to water is much lower than the attractions for either the water to other water molecules or the oil to other oil molecules. If we carefully pour the two different substances together, they will form two layers, oil floating on more dense water. These layers will be fairly homogeneous, with a small amount of mixing at the interface (junction between the two layers) due to some molecules escaping the attractions of their similar neighbors due to higher than average kinetic energy. If we blend the oil and water well with a mixer, we can use mechanical energy to separate the molecules into small droplets. Oil droplets are dispersed in water and water droplets are dispersed in oil, but the similar molecules in any given droplet have stronger intermolecular attractions for each other than for the other type of molecule outside the droplet. The droplets move in the liquid phase, partly by random collective molecular motion called Brownian motion and partly by density differences. A less dense oil droplet displaces an equal volume of more dense water which makes it more buoyant. With time, similar droplets will collide and stick together to form larger drops. The oil will gradually move to the top of the mixture. The oil and water will separate into two layers. When we say “oil and water don’t mix” we really mean that oil and water don’t stay mixed. Personification (dangerous but tempting) gives us a discouraging view of the liquids in a mixture: they behave like parochial little droplets eschewing the company of those different from themselves. With their strong intermolecular attractions for their own kind how can any liquids ever form solutions? If all the possible mixtures of liquids are lined up in a spectrum, on the end opposite from

the oil/water mixture is the mixture of water and ethanol (grain alcohol). Ethanol is a polar compound with this molecular geometry:

Because it has an oxygen-hydrogen covalent bond, this compound is able to undergo the strongest intermolecular attraction, hydrogen bonding. Due to these hydrogen bonds, ethanol is a liquid at room temperature and pressure. Unlike the oil and water mixture, ethanol and water are miscible, or mutually soluble in any proportions. If a drop of ethanol is added to water, it will spread by diffusion to form a perfectly uniform mixture, and, if a drop of water is added to ethanol, it will spread by diffusion to form a perfectly uniform mixture. If any proportion of water and ethanol are combined they will spread out, mix, and stay mixed. What is the difference between oil and water versus ethanol and water? For two liquids to be soluble, they must have similar strength intermolecular attractions for each other as each has for itself. Ethanol and water mix because the hydrogen bond strength for the ethanol to the water is similar to the hydrogen bond strength for water to itself and for ethanol it itself. Chemists use the aphorism “like dissolves like” to summarize this trend. Non-polar liquids will form solutions, too. An example is using turpentine to thin oil paint. The attractions of the solute to the solvent don’t have to be strong, they just have to be similar in strength to the attractions of the pure liquids. Concept Check: Elemental bromine is a liquid at STP. Which of these will dissolve bromine better, water or hexane (the formula for hexane is C6H14)? Answer: The hexane will dissolve bromine better. Water is polar and hydrogen bonding. Bromine, Br2, is non-polar. Hexane is also non-polar. “Like dissolves like” so the two non-polar substances will mix better. This is not because the bromine is strongly attracted to the hexane or vice-versa. The bromine and hexane mix better than the bromine and water because the water is strongly attracted to itself and only weakly attracted to the bromine. It is really a case of the water resisting mixing with the bromine.

Emulsions Oil and water can be forced to mix. We see this in the kitchen when we make mayonnaise or when we use liquid detergent to clean greasy dishes. Mayonnaise is an emulsion or a stable suspension of insoluble liquids (they technically don’t have to be liquids, but that is the common usage). Mayonnaise is oil and vinegar (mostly water) with egg yolk added as a stabilizer. The egg yolk contains a protein which has both polar and non-polar parts. The non-polar sections of the protein mix with the oil droplets and the polar parts mix with the water in vinegar. Soap another molecule that allows oil to mix with water. Soap is an ionic salt made from the reaction of a fatty acid (a high molecular weight organic acid found in fat) and sodium hydroxide (old fashioned lye). The Babylonians made soap six thousand years ago. A soap molecule has a non-polar part consisting of a long chain of carbon and hydrogen atoms and a polar part consisting of two oxygen atoms bonded to a carbon atom (that atom group has a negative charge) and a sodium ion.

Water is attracted to the polar/ionic part of the molecule but not the hydrocarbon part. The hydrocarbon part mixes well with oil, though. Soap and other similar molecules are called surfactants. A surfactant is a molecule that acts on a solvent to decrease its surface tension by disturbing the solvent’s intermolecular forces. Surfactants have polar and non-polar molecular regions. Surfactants tend to arrange themselves along boundaries between phases with their polar portions facing the water phase and their non-polar portions facing the oil phase. If one of the phases is dispersed in the other, the droplets will form micelles, or organized clusters.

Solid Solutes in a Liquid Solvent Often, it is useful to think of solubility as being a range of possibilities all the way from miscible to immiscible. The amount of solute can be quantified rather than all or nothing. We will discuss the concept of concentration of solutions in the next section. An increase in temperature increases the amount of solid that will dissolve in a liquid for many solutes (but not all). Conceptually this is because at higher temperatures the solvent has more kinetic energy available to overcome its own and the solute’s intermolecular attractions so as to separate the pure phases. An increase in temperature decreases solubility of some substances, though. An example is calcium carbonate, or lime scale. Calcium carbonate is the main component of the mineral deposits that form in water heaters and coffee makers in areas with hard water. This ionic solid is less soluble in hot water and forms precipitates in household appliances that heat water. Pressure has little or no effect on the solubility of solids and liquids in a liquid solvent.

Molecular Solids: The process of dissolving a molecular solid in a liquid is the same as for dissolving

two liquids: “like dissolves like.” A molecular solid will dissolve in a liquid if the strength of intermolecular force that holds the solid together is similar to the strength of the intermolecular force it has with the solvent. The intermolecular forces in a solid are fairly strong (or it would be a gas instead of a solid). The forces between the solid and the solvent must be fairly strong as well. Sugar (sucrose) is a polar molecular solid that is able to hydrogen bond. It is soluble in water because sugar and water form strong hydrogen bonds together.

Metallic Solids: Metallic solids are not soluble in molecular liquids. Note that this is solubility we are talking about rather than chemical reaction. A metal can react with an aqueous solute as in the single displacement reaction of a metal with an ionic compound. When they react, the metal looks like it disappears; we even casually refer to an acid ‘dissolving’ a metal. But these are chemical reactions, and they form new substances with different properties. A chemical reaction causes a new substance to be formed, but a solution is a mixture each component retaining its own identity. The properties of the mixture are similar to the properties of each component. Back to mixtures: a metal will not dissolve in a molecular liquid because it does not have metallic bonds. A metal will dissolve in liquid mercury or in another metal that is molten. Miners used liquid mercury to recover gold in California during the gold rush of the mid-1800s. Tiny particles of gold would dissolve in the mercury and form an alloy, which was easier to separate from the rock, gravel, and water from the mining operations. The alloy was heated to drive off the mercury leaving the gold behind. Some parts of Northern California are seriously contaminated with mercury waste from this process. See the USGS fact sheet “Mercury Contamination from Historic Gold Mining in California” for more information or read first hand accounts in Roughing It by Mark Twain.

Network Covalent Solids: Network covalent compounds also tend not to dissolve in a molecular liquid (reactions aside). The particles that make up a network covalent solid like graphite tend to be too large to remain dispersed in a liquid. They eventually settle out. If the solvent breaks apart the particles this is really a chemical reaction since covalent bonds are broken. Graphite is soluble in molten metals (formation of carbon steel, for example) and in some conducting polymers.

Ionic Solids: Some ionic compounds will dissolve in polar solvents by ion-dipole forces. If so, the stabilization that the ions receive from the dipole interactions has to be similar in strength to the stabilization that they receive by being in a crystal lattice.

Solid as a Solvent Mixtures can be formed in which a solid substance is the major component. The easiest examples to think of are heterogeneous mixtures like concrete, but solids

can also form homogeneous mixtures.

Gas Solutes in a Solid Solvent Heterogeneous mixture is like foamed polystyrene or Styrofoam®. When the gas bubbles are dispersed throughout a liquid that freezes or, in the case of polymers, solidifies as the chemical reactions progresses. Gases can for homogeneous mixtures with solids. One important example is hydrogen dissolved in palladium. The hydrogen gas molecules are small enough to slip between metal atoms in the palladium crystal lattice. There is a weak attraction between the gas and the metal which is sufficient to keep the hydrogen in the lattice. Palladium catalysts are referred to as “hydrogen sponges”. Palladium is used as a catalyst in reactions that add hydrogen to multiple bonds on organic molecules.

Liquid Solutes in a Solid Solvent Adsorption is the accumulation of a thin film of a liquid (or gas) on the surface of a solid. Absorption is the accumulation of liquid (or gas) in the bulk of a solid. Weak intermolecular attractions cause both phenomena, but, in absorption, the liquid is able to penetrate throughout the solid. Pesky old water can and does adsorb on any solids that are exposed to air. In a relatively humid environment, the amount of water that clings to laboratory chemicals and glassware can cause significant errors due to masses reading high. In lab experiments in which the mass readings need to be accurate to two or more decimal places, solids are usually placed in an oven and subjected to low heat to evaporate the adsorbed water. Water will also absorb into many solids if the holes in the crystal structure are large enough or if it is porous. Hydrates are ionic compounds that absorb water and incorporate it into their crystal structure in regular repeatable quantities. The ion-dipole forces in the crystal can stabilize the crystal structure enough to be similar to a chemical reaction. Some hydrates are different colors than the anhydrous form because of the lower energy due to the stabilizing effect of the water. Hygroscopic solids are those that absorb water strongly. Some will absorb enough water from humid air to form a solution; they appear to “melt” if left out in the atmosphere.

Solid Solutes in a Solid Solvent Most metals are not liquids at STP. Homogeneous mixtures of solid metals are called alloys. These are blended while the metals are in a liquid phase then cooled to solidify. The properties of the mixture may be very different from the properties of the pure substances, and changing the relative amounts of the components can have a big impact on the properties of the mixture. White cast iron is 3% carbon and 97% iron; steel is 1% carbon and 99% iron. Adding less carbon makes steel denser (7.83 versus 7.60 g/cm3) and gives it a higher melting point (1430 versus 1130 °C) than cast iron.

Home | Gas Laws | KMT | IMF | Liquids | Solids | Phase | Mixtures | Concentration | Colligative Prop

© Copyright 2005, Kelley Whitley, ChemProfessor. All rights reserved. This site was last updated 01/12/06